Measurement and Geometry
Measurement and Geometry are presented together to emphasise their relationship to each other, enhancing their practical relevance. Students develop an increasingly sophisticated understanding of size, shape, relative position and movement of two-dimensional figures in the plane and three-dimensional objects in space. They investigate properties and apply their understanding of them to define, compare and construct figures and objects. They learn to develop geometric arguments. They make meaningful measurements of quantities, choosing appropriate metric units of measurement. They build an understanding of the connections between units and calculate derived measures such as area, speed and density.(ACARA, 2012)
Year 1 -Tell time to the half hour (ACMMG020) -Reading time on analogue and digital clocks and observing the characteristics of half hour times Year 2 -Tell time to the quarter hour, using the language of 'past' and 'to' (ACMMG039) -Describing the characteristics of quarter past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three Year 3 -Tell time to the minute and investigate the relationship between units of time (ACMMG062) -Recognising there are 60 minutes in an hour and 60 seconds in a minute (ACARA, 2012)
Content Discriptors from Australian Mathmatics Curriclum
Foundation
Year 1
Year 2
Year 3
Measurement and Geometry - Using units of Measurement
- Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language
- Compare and order the duration of events using the everyday language of time
- Connect days of the week to familiar events and actions
- Measure and compare the lengths and capacities of pairs of objects using uniform informal units
- Tell time to the half hour
- Describe duration using months, weeks, days and hours
- Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units
- Compare masses of objects using balance scales
- Tell time to the quarter-hour, using the language of ‘past’ and ‘to’
- Name and order months and seasons
- Use a calendar to identify the date and determine the number of days in each month
- Measure, order and compare objects using familiar metric units of length, mass and capacity
- Tell time to the minute and investigate the relationship between units of time
Number and Algebra - Fractions and decimals
- Recognise and describe one-half as one of two equal parts of a whole.
- Recognise and describe one-half as one of two equal parts of a whole.
- Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Number and Algebra – Number and Place Value
- Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point
- Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond
- Subitise small collections of objects
- Represent practical situations to model addition and sharing
- Compare, order and make correspondences between collections, initially to 20, and explain reasoning
- Develop confidence with number sequences to and from 100 by ones from any starting point.
- Skip count by twos, fives and tens starting from zero
- Recognise, model, read, write and order numbers to at least 100.
- Locate these numbers on a number line
- Count collections to 100 by partitioning numbers using place value
- Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts
- Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences.
- Recognise, model, represent and order numbers to at least 1000
- Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting
- Explore the connection between addition and subtraction
- Solve simple addition and subtraction problems using a range of efficient mental and written strategies
- Recognise and represent multiplication as repeated addition, groups and arrays
- Recognise and represent division as grouping into equal sets and solve simple problems using these representations
- Investigate the conditions required for a number to be odd or even and identify odd and even numbers
- Recognise, model, represent and order numbers to at least 10 000
- Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
- Recognise and explain the connection between addition and subtraction
- Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
- Recall multiplication facts of two, three, five and ten and related division facts
- Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies
(ACARA, 2012)
Number and Algebra
Number and Algebra are developed together, as each enriches the study of the other. Students apply number sense and strategies for counting and representing numbers. They explore the magnitude and properties of numbers. They apply a range of strategies for computation and understand the connections between operations. They recognise patterns and understand the concepts of variable and function. They build on their understanding of the number system to describe relationships and formulate generalisations. They recognise equivalence and solve equations and inequalities. They apply their number and algebra skills to conduct investigations, solve problems and communicate their reasoning.(ACARA, 2012)
Foundation – Year 2 The early years (5–8 years of age) lay the foundation for learning mathematics. Students at this level can access powerful mathematical ideas relevant to their current lives and learn the language of mathematics, which is vital to future progression. Children have the opportunity to access mathematical ideas by developing a sense of number, order, sequence and pattern; by understanding quantities and their representations; by learning about attributes of objects and collections, position, movement and direction, and by developing an awareness of the collection, presentation and variation of data and a capacity to make predictions about chance events. Mathematics Organisation ACARA | The Australian Curriculum | Version 3.0 dated Monday, 23 January 2012 6 Understanding and experiencing these concepts in the early years provides a foundation for algebraic, statistical and multiplicative thinking, that will develop in subsequent mathematical questions about their world, to identify simple strategies to investigate solutions, and to strengthen their reasoning to solve personally meaningful problems. (ACARA, 2012)
Years 3–6 These years emphasise the importance of students studying coherent, meaningful and purposeful mathematics that is relevant to their lives. Students still require active experiences that allow them to construct key mathematical ideas, but also gradually move to using models, pictures and symbols to represent these ideas. The curriculum develops key understandings by extending the number, measurement, geometric and statistical learning from the early years; by building foundations for future studies through an emphasis on patterns that lead to generalisations; by describing relationships from data collected and represented; by making predictions; and by introducing topics that represent a key challenge in these years, such as fractions and decimals. In these years of schooling, it is particularly important for students to develop a deep understanding of whole numbers to build reasoning in fractions and decimals and to develop a conceptual understanding of place value. These concepts allow students to develop proportional reasoning and flexibility with number through mental computation skills, and to extend their number sense and statistical fluency. (ACARA, 2012)
Measurement and Geometry are presented together to emphasise their relationship to each other, enhancing their practical relevance. Students develop an increasingly sophisticated understanding of size, shape, relative position and movement of two-dimensional figures in the plane and three-dimensional objects in space. They investigate properties and apply their understanding of them to define, compare and construct figures and objects. They learn to develop geometric arguments. They make meaningful measurements of quantities, choosing appropriate metric units of measurement. They build an understanding of the connections between units and calculate derived measures such as area, speed and density.(ACARA, 2012)
Year 1
- Tell time to the half hour (ACMMG020)
- Reading time on analogue and digital clocks and observing the characteristics of half hour times
Year 2
- Tell time to the quarter hour, using the language of 'past' and 'to' (ACMMG039)
- Describing the characteristics of quarter past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three
Year 3
- Tell time to the minute and investigate the relationship between units of time (ACMMG062)
- Recognising there are 60 minutes in an hour and 60 seconds in a minute
(ACARA, 2012)
Content Discriptors from Australian Mathmatics Curriclum
Measurement
- Compare and order the duration of events using the everyday language of time
- Connect days of the week to familiar events and actions
- Tell time to the half hour
- Describe duration using months, weeks, days and hours
- Compare masses of objects using balance scales
- Tell time to the quarter-hour, using the language of ‘past’ and ‘to’
- Name and order months and seasons
- Use a calendar to identify the date and determine the number of days in each month
- Tell time to the minute and investigate the relationship between units of time
and
decimals
- Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond
- Subitise small collections of objects
- Represent practical situations to model addition and sharing
- Compare, order and make correspondences between collections, initially to 20, and explain reasoning
- Skip count by twos, fives and tens starting from zero
- Recognise, model, read, write and order numbers to at least 100.
- Locate these numbers on a number line
- Count collections to 100 by partitioning numbers using place value
- Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts
- Recognise, model, represent and order numbers to at least 1000
- Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting
- Explore the connection between addition and subtraction
- Solve simple addition and subtraction problems using a range of efficient mental and written strategies
- Recognise and represent multiplication as repeated addition, groups and arrays
- Recognise and represent division as grouping into equal sets and solve simple problems using these representations
- Recognise, model, represent and order numbers to at least 10 000
- Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
- Recognise and explain the connection between addition and subtraction
- Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
- Recall multiplication facts of two, three, five and ten and related division facts
- Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies
Number and Algebra
Number and Algebra are developed together, as each enriches the study of the other. Students apply number sense and strategies for counting and representing numbers. They explore the magnitude and properties of numbers. They apply a range of strategies for computation and understand the connections between operations. They recognise patterns and understand the concepts of variable and function. They build on their understanding of the number system to describe relationships and formulate generalisations. They recognise equivalence and solve equations and inequalities. They apply their number and algebra skills to conduct investigations, solve problems and communicate their reasoning.(ACARA, 2012)
Foundation – Year 2
The early years (5–8 years of age) lay the foundation for learning mathematics. Students at this level can access powerful mathematical ideas relevant to their current lives and learn the language of mathematics, which is vital to future progression.
Children have the opportunity to access mathematical ideas by developing a sense of number, order, sequence and pattern; by understanding quantities and their representations; by learning about attributes of objects and collections, position, movement and direction, and by developing an awareness of the collection, presentation and variation of data and a capacity to make predictions about chance events.
Mathematics Organisation
ACARA | The Australian Curriculum | Version 3.0 dated Monday, 23 January 2012 6
Understanding and experiencing these concepts in the early years provides a foundation for algebraic, statistical and multiplicative thinking, that will develop in subsequent mathematical questions about their world, to identify simple strategies to investigate solutions, and to strengthen their reasoning to solve personally meaningful problems. (ACARA, 2012)
Years 3–6
These years emphasise the importance of students studying coherent, meaningful and purposeful mathematics that is relevant to their lives. Students still require active experiences that allow them to construct key mathematical ideas, but also gradually move to using models, pictures and symbols to represent these ideas.
The curriculum develops key understandings by extending the number, measurement, geometric and statistical learning from the early years; by building foundations for future studies through an emphasis on patterns that lead to generalisations; by describing relationships from data collected and represented; by making predictions; and by introducing topics that represent a key challenge in these years, such as fractions and decimals.
In these years of schooling, it is particularly important for students to develop a deep understanding of whole numbers to build reasoning in fractions and decimals and to develop a conceptual understanding of place value. These concepts allow students to develop proportional reasoning and flexibility with number through mental computation skills, and to extend their number sense and statistical fluency. (ACARA, 2012)